Even if it was currently working for me, it would be bloody difficult or slow to snip something from a media file interview which lacks a transcription of that episode, so as to reference what one is supposedly commenting upon. Thus:

Sean Carroll wrote:I have previously mentioned the idea that the thermodynamic arrow of time — the fact entropy is very small in the past, and tends to grow on purely statistical grounds — is responsible for the fact that we can remember the past but not the future. But why is that exactly? . . . the basic idea hinges on the consistency of different hypotheses about what was going on in the far past. In particular, imagine a situation where we have three things: 1) a memory of receiving a new sweater for Christmas last year, 2) detailed knowledge of the laws of physics, and 3) complete ignorance about the initial conditions of the universe, i.e. a hypothesis that all conditions consistent with our current macroscopic state are equally likely. . . . Can we conclude, from these three pieces of information, that we probably did receive a sweater? No; in fact, it turns out to be incredibly unlikely. That’s because, of all the ways we could have a memory of receiving the sweater, most involve very high-entropy conditions in the past, out of which we and our memory have appeared very recently as a random fluctuation. Random fluctuations of order from disorder are very rare; however, there are many many more ways to be disordered than to be ordered, so the number of ways to achieve order is dominated by trajectories that come from disorder, not trajectories that come from greater order. So if we really believe that all possible past configurations are equally likely, our “memories” are utterly unreliable.

What saves us from such a psychologically devastating situation is that this set of beliefs is cognitively unstable. That’s because we used our knowledge of the laws of physics (not to mention the rules of logic, probability, and so forth) to reach this conclusion. But the reason why we believe these laws is that we have memories of experiments that count as evidence for them — but these memories are completely unreliable! So we have no reason to think that we actually understand the laws of physics. Thus, this set of beliefs is self-undermining; if we hold it, we conclude that we have no reason to hold it.

The way out is to change our initial set of assumptions. We simply replace the assumption that any past configuration is equally likely with the “past hypothesis” — the idea that the early universe is in a very special state (or one of a small number of special states) with very low entropy. This simple hypothesis removes from consideration all of the thermodynamically unlikely (but very numerous) possible histories in which we and our memories of Christmas past are just fluctuations from the surrounding chaos. Given that we have a memory of receiving a sweater, and that the universe began in a highly ordered state, it is quite likely that we actually did receive a sweater. [from his blog entry "WHAT WE KNOW, AND DON'T, AND WHY"]

Sean Carroll favors eternalism, where the flow of time [not the organization of time] is a psychological illusion. Possibly resulting, IMO, from the brain's dimensionally extended cognitive structure being divided into distinct units which can only "know" the neural states of their particular slices, or applicable sequences of such. IOW, there's no cognition available for simultaneously apprehending the entire framework of time-ordered events constituting a human lifetime.

Of course, the question still arises as to why the arrow of this "mental flow" is biased toward the future. It might be because that is the direction where the biological infestation on Earth grows and develops in complexity, rather than the reverse of brained macroscopic life increasing in vulnerability and inching toward certain rather than merely possible doom. Or perhaps language (which realizes so much of human thought) actually couldn't express its semantic duties properly if the flux conformed to a pastwards psychological arrow?

At any rate, despite the illusion status being promoted by many physicists themselves, they aren't comfortable crouching it entirely in the context of brain and consciousness. So they garble-up the "flow isn't objective" declaration by venturing into thermodynamic territory, etc. Excusable, since Boltzmann's work came before these consequences that fell out of Einstein's; and scientists often care less about later issues of compatibility / commensurability between assorted views and models than the more immediately important agenda of achieving consistency within each individual one (that they're fiddling with).